1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
运筹学 Operations Research
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MA210
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
英文 English
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
张进 数学系
慧园 3 栋 509
zhangj9@sustc.edu.cn
0755-88015915
Jin Zhang, Department of Mathematics,
Block 3 Room 509, Wisdom Valley.
zhangj9@sustc.edu.cn
0755-88015915
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
（请保留相应选项 Please only keep the relevant information）
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
授课方式
Delivery Method
讲授
Lectures
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
46
N/A
46
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
数学分析 III 或数学分析精讲
Mathematical Analysis III or Real Analysis
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
是数学系和金融数学系金融数学及金融工程等课程的先修课程，同时也是其他工程学科多
门专业课的先修课程。
It is a pre-requisite course for courses in finance mathematics and financial engineering in the
Department of Mathematics and Financial Mathematics. It is also a pre-requisite course for many
professional courses in other engineering disciplines.
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
运筹学主要向学生系统地讲授线性规划、无约束优化、约束优化、多目标优化、整数规划等运筹学建模和基本优化方法，
同时包括运筹学模型的模型条件、结构特点、基本方法步骤及应用范围等；使学生认识到运筹学模型和优化应用在实践中
的重要性，领会其基本思想和分析、解决问题的思路。
Operational research mainly teaches the students the systematical methods of operational research and basic optimization, including
linear programming, unconstrained optimization, constrained optimization, multi-objective programming and integer programming. It
also contains some operational research models, such as model conditions, structure features, basic steps, application scope, etc.
Operational research makes the students realize the importance of the operation research modeling and optimization applications in
practice, understand the thought of the basic ideas and analysis when solving problems
16.
预达学习成果 Learning Outcomes
通过对本课程的学习，学生可以达到以下基本要求：
1.掌握线性规划、约束优化、多目标优化、动态规划、整数规划等运筹学模型；
2.通过对具体方法与模型的学习，认识运筹学在经营管理决策中作为提高决策水平的方法和作用；
3.了解运筹学模型以及主要的相关优化方法；
4.领会运筹学在分析与解决实际问题过程中的基本思想和的基本思路，并进行以实际应用为导向的训练。
After completing this course, students should meet the following basic requirements:
1. Master the operational research model, such as linear programming, constrained programming, multi-objective programming,
dynamic programming and integer programming;
2. Recognize the operational research’s effects that was used as the methods and tools to improve the level of decision-making in the
management decisions, throughout the specific methods and models of learning;
3. Understand the operational research models and master the related optimization methods;
4. Comprehend the basic idea and thought of operational research that are used in analyzing and solving the actual problems, carry
on the training of the practical-oriented application.
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
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1． 优化概论（4 学时）
Introduction to optimization (4 hours)
2． 线性规划和单纯形法（5 学时）
Linear programming and the Simplex Method (5 hours)
3． 无约束优化方法（7 学时）
Unconstrained optimization methods (7 hours)
4． 非线性优化基础：（6 学时）
Basics of nonlinear optimization: (6 hours)
5． 约束优化方法（8 学时）
Constrained optimization methods (8 hours)
6． 多目标优化（4 学时）
Multi-objective programming (4 hours)
7． 整数规划（4 学时）
Integer programming (4 hours)
8． 动态规划（4 学时）
Dynamic programming (4 hours)
9． 专题一：运筹学与数据科学（2 学时）
Special topic I: operational research and data science (2 hours)
10．专题二：运筹学与博弈论（2 学时）
Special topic II: operational research and game theory (2 hours)
每周进度 weekly schedule:
第 1 周：优化体系、类型以及全局最优解和局部最优解（4 学时）
Week 1: optimization terms, types, and global vs local solutions (4 hours).
第 2 周：线性规划问题及数学模型（2 学时）
Week 2: linear programming (2 hours).
第 3 周：单纯形法原理及计算步骤、极值点、基本可行解,等（3 学时）。凸函数与凸集合（1 学时）
Week 3: concepts of extreme point, basic feasible solution, etc (3 hours). Convex function and convex set (1 hour).
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第 4 周：梯度下降算法（2 学时）
Week 4: Gradient descent method (2 hours).
第 5 周：牛顿型法（2 学时）和拟牛顿法（2 学时）。
Week 5: Newton method (2 hours) and quasi-Newton methods (2hours).
第 6 周：约束优化问题的必要性条件（2 学时）
Week 6: necessary optimality conditions of constrained optimization (2 hours).
第 7 周：约束优化问题的充分性条件（2 学时）与凸优化的 KKT 条件（2 学时）。
Week 7: sufficient optimality conditions of constrained optimization (2 hours) and KKT conditions for convex optimization (2
hours).
第 8 周：罚函数法(2 学时)。
Week 8: penalty function method (2 hours).
第 9 周：障碍函数法（2 学时）与梯度投影法（2 学时）。
Week 9: barrier function method (2 hours) and gradient projection method (2 hours).
第 10 周：增广拉格朗日法（2 学时）。
Week 10: Augmented Lagrangian method (2 hours).
第 11 周：多目标优化的模型介绍（1 学时）、求解方法和应用（3 学时）。
Week 11: introduction to multi-objective programming (1hour), solution schemes and applications (3 hours).
第 12 周：专题一：运筹学与数据科学（2 学时）
Week 12: special topic I: operational research and data science (2 hours)
第 13 周：整数规划模型的介绍（1 学时）、分支定界法（2 学时）、0-1 规划（1 学时）
Week 13: introduction to integer programming (1 hour)，branch-and-bound method (2hours)，binary programming (1 hour)
第 14 周：专题二：运筹学与博弈论（2 学时）
Week 14:Special topic II: operational research and game theory (2 hours)
第 15 周：动态规划模型介绍（1 学时）、求解方法和应用（3 学时）.
Week 15: introduction to dynamic programming (1hour)，solution schemes and applications (3hours).
18.
教材及其它参考资料 Textbook and Supplementary Readings
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Supplementary Readings:
1） An Introduction to Optimization, 4th Edition, by Chong and Zak
2） Undergraduate nonlinear continuous optimization, lecture notes, by James V Burke, University of Washington
3) An easy path to convex analysis and applications, by Mordukhovich and Nam
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class
Performance
小测验
Quiz
课程项目 Projects
平时作业
Assignments
20%
期中考试
Mid-Term Test
20%
期末考试
Final Exam
2 小时
2 hours
60%
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
□
✔
B. 二级记分制（通过/不通过） Pass/Fail Grading
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority
